ShufflingCardsDiv1

Fox Ciel likes shuffling cards. She uses a deck with 2N cards, numbered 1 through 2N. Initially, this deck is sorted: the cards are in the order 1,2,3,...,2N from top to bottom.
Ciel always uses the same procedure when shuffling. One round of shuffling looks as follows:

1. She splits the deck into two piles: the top N cards will be pile A, the bottom N cards pile B.
2. She takes pile A and rearranges the cards it contains arbitrarily.
3. She takes pile B and rearranges the cards it contains arbitrarily.
4. She interleaves the cards from the two piles, producing a single deck again. More precisely, if pile A has cards A1,A2,...,AN and pile B has cards B1,B2,...,BN then the new deck will be A1,B1,A2,B2,...,AN,BN. (Note that the first card must be from pile A.)

For example, let N=2 and suppose that Ciel starts with the sorted deck 1,2,3,4. After the first round of shuffling, she can produce one of the following four decks:

• 1,3,2,4
• 1,4,2,3
• 2,3,1,4
• 2,4,1,3

You are given a int[] permutation which contains a permutation of the 2N cards. Ciel wants to produce this permutation of her deck. Compute and return the smallest number of rounds of shuffling she has to perform. (When rearranging a pile during the shuffling, she can always pick the best possible order of those cards.) If Ciel cannot reach the given permutation by shuffling, return -1 instead.